Question

Identify the 42nd term of an arithmetic sequence where a1 = -12 and a27 = 66

Answer 1

find \( d\) from the information

Answer 2

\(\large \begin{align} \color{black}{a_{1},a_{2},a_{3},a_{4}\cdot \cdot \cdot \cdot \infty \hspace{.33em}\\~\\
\implies a_{1},a_{1}+d,a_{1}+2d,a_{1}+3d \cdot \cdot \cdot \cdot \infty \hspace{.33em}\\~\\
a_{1}=-12 \hspace{.33em}\\~\\
a_{27}=66 \hspace{.33em}\\~\\
a_{27}=a_1+26d \hspace{.33em}\\~\\
a_{42}=a_1+41d \hspace{.33em}\\~\\
}\end{align}\)

Answer 3

nth term of an AP is given by...
\[a_{n}=a+(n-1)d\]\[a=-12\]
for n=27,
\[a{_{27}}=a+(27-1)d\] put the value of a and a27
\[66=-12+26d\]
calculate d from this equation
then for n=42,
\[a_{42}=a+(42-1)d\]\[a_{42}=a+41d\]
put the values of a and d and calculate a42